1. 8 Stars … how I wonder what you are.

2. 8 Goals Stars are Suns. Are they: –Near? Far? –Brighter? Dimmer? –Hotter? Cooler? –Heavier? Lighter? –Larger? Smaller? What categories can we place them in?

3. 8 Angular Size Linear size = how big something really is –Meters, inches, light years, feet Angular size = how big something looks –Degrees, arcminutes, arcseconds, milliarcseconds Circle = 360 degrees 1 degree = 60 arcmin 1 arcmin = 60 arcsec 1 arcsec = 1000 mas

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5. 8 Distance One proof of a heliocentric Universe is stellar parallax. –Tycho Brahe saw no parallax. –Copernicus: stars too far away. Nearest star: Proxima Centauri Parallax angle = 0.76 arcsec –Tycho’s precision = 1 arcmin

6. 8 The Parsec What is the distance of an object with a parallax angle of 1 arcsec? Distance = 206,265 AU This distance is 1 parsec (pc) 1 pc = 206,265 AU = 3.3 ly 1 lightyear = distance light travels in one year.

7. 8 Distances Closest star: Proxima Centauri parallax = 0.76 arcsec Distance = 1.3 pc or 4.3 lightyears

8. 8 Brightness How bright are they really? What is due to distance? What is due to luminosity? Luminosity: –Total energy radiated every second.

9. 8 Magnitude Scale The SMALLER the number the BRIGHTER the star! –Every difference of 1 magnitude = 2.5x brightness. –Every difference of 5 magnitudes is a 100x difference in brightness.

10. 8 Magnitude vs. Brightness Mag. Difference Factors of 2.5Brightness Diff. 12.5 1 = 2.5 2.5 22.5 2 = 2.5 X 2.5 6.3 32.5 3 = 2.5 X 2.5 X 2.5 16 42.5 4 = 2.5 X 2.5 X 2.5 X 2.5 40 52.5 5 = 2.5 X 2.5 X 2.5 X 2.5 X 2.5 100 62.5 6 = 2.5 X 2.5 X 2.5 X 2.5 X 2.5 X 2.5 250

11. 8 Star light, star bright Sirius is magnitude -1.5 Polaris is magnitude 2.5 Is Sirius really more luminous than Polaris? No, Sirius is just closer.

12. 8 Apparent and Absolute Apparent Magnitude = brightness (magnitude) of a star as seen from Earth.  m –Depends on star’s total energy radiated (Luminosity) and distance Absolute Magnitude = brightness (magnitude) of a star at a distance of 10 pc.  M –Only depends on a star’s luminosity

13. 8 example Our Sun: –m = -26.8, –distance = 4.8 x 10 -6 pc So: M = 4.8 Polaris: –m = 2.5, –distance = 132 pc So: M = -3.1 Polaris is 1500 times more luminous than the Sun!

14. 8 Stellar Spectra Stellar Temperatures How hot are stars? In Lecture 4 we learned about thermal radiation and temperature. Since different stars have different colors, different stars must be different temperatures. Hot Cool

15. 8 Spectral Classification

16. 8 Stellar Masses How massive are stars? Kepler’s Laws – devised for the planets. Apply to any object that orbits another object. Kepler’s Third Law relates: – Period: “how long it takes to orbit something” –Semimajor axis: “how far you are away from that something” –Mass: “how much gravity is pulling you around in orbit” Where M is the Total Mass. Can calculate the mass of stars this way.

17. 8 Binary Stars Most stars in the sky are in multiple systems. Binaries, triplets, quadruplets, etc…. –Sirius –Alcor and Mizar –Tatooine The Sun is in the minority by being single.

18. 8 0.005 arcsec

19. 8 Stellar Masses How massive are stars? Most stars have masses calculated this way. Result: –The more massive the star, the more luminous it is. –The more massive the star, the hotter it is.

20. 8 Stellar Radii How big are stars? We see stars have different luminosities and different temperatures. Stars have different sizes. If you know: –Distance –Angular size Learn real size. 50 mas

21. 8 Betelgeuse Angular size = 50 mas Parallax = 7.6 mas = 0.0076 arcsec Apparent mag = 0.6 Distance = 1/parallax = 132 pc True size = distance * angular size = 1400 R sol Absolute Mag = m – 5log(d/10pc) = -5 –Our sun M ~5, Betelgeuse = 10,000x luminosity

22. 8 Angular versus Linear Supergiants, Giants and Dwarfs

23. 8 H-R Diagram Can order the stars we see by: –Temperature (or spectral type) –Luminosity (or absolute magnitude). And see where other qualities fall: –Mass –Radius

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25. 8 The Main Sequence Stars characterized by what holds them up. 90% held up by heat of Hydrogen fusion? 4H  He + Energy

26. 8 Main Sequence & Thermal Radiation The Main Sequence makes sense! Hotter stars are bluer – Wien’ Law Hotter stars are brighter – Stefan’s Law

27. 8 Homework #8 For Feb 12: Read B16.6, 17.1 – 17.2, Ty10 Do Ch16 Problems: 6, 9, 21